On N, the relation R is a R b if a + b = 10. Which of these describes R?

Question 31

MediumOriginal question

On $\mathbb{N}$ , the relation $R$ is $a \mathrel{R} b$ if $a + b = 10$ . Which of these describes $R$ ?

Reflexive and symmetric, but not transitiveCorrect answerYour answerNeither reflexive, symmetric nor transitiveCorrect answerYour answerSymmetric and transitive, but not reflexiveCorrect answerYour answerSymmetric onlyCorrect answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

$1 + 1 \ne 10$ , so 1 is not related to itself: not reflexive. $a + b = b + a$ : symmetric.
1 and 9 are related, 9 and 1 are related, but $1 + 1 \ne 10$ : not transitive.

Worth noting

Only 5 is related to itself, so the relation cannot be reflexive on all of $\mathbb{N}$ .

Concept: Testing a relation given by a rule
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On N\mathbb{N}N, the relation RRR is aRba \mathrel{R} baRb if a+b=10a + b = 10a+b=10. Which of these describes RRR?

Explanation

On $\mathbb{N}$ , the relation $R$ is $a \mathrel{R} b$ if $a + b = 10$ . Which of these describes $R$ ?